Since the clapping is not perfectly consistent, we may not be able to make an exact prediction, but we can reach a reasonable range of predictions.

By looking at the available data, we can make a very reasonable line of best fit, which will best represent the overall trend of the experiment.

Then I like to show a visualization of these concepts in a PowerPoint Presentation. Afterward, I hand out an introductory problem template, so that students can solve a similar problem with me: Line of Best Fit Intro. I ask the students to draw the line of best fit as an estimate of the equation. Then, we follow up with the process on the graphing calculator (I like to demonstrate the process with the TI-Smartview software). This is just a brief demo. I will give the students calculators for the second half of the lesson and detailed instructions on how to use the technology.

We conclude by comparing the line we drew by hand and the line drawn by the calculator and discuss how close they are to each other.

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As we move on, I first ask students to review the Introduction Problem with their own graphing calculator. Students work in partners to find the line of best fit on their calculators. I give them this refrence sheet: Line of Best Fit Instructions.docx

When they are finished, I check their work with a quick look at their calculators. Then, I give the pair a copy of the Linear Fit Partner Quiz. My rules for a partner quiz are quite simple: you can whisper to your partner as you work, but you must both work. I don't want students to distribute the problems between them, but solve each problem together. I expect to see both students write on each problem and often give out different colored pencils to my students so that they can color code their individual work.

Technology Note: My students are each assigned a graphing calculator. Since they often forget their own number, I sometimes print out tickets that tell them which calculator they are assigned to calc number template.docx.

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After the partner quiz I plan to spend a brief amount of time reviewing misconceptions that I noticed during the quiz. These might be issues that students asked me about or mistakes that they had made in their work. I like to give this feedback right away, so I collect the work from the class and review a few problems on the board.

I end up reviewing this problem because students get confused when none of the choices match the line of best fit generated by their calculator. Typically, my students work together to enter all the data points into the graphing calculator. Then, they create a line of best fit. Thus, the graphs on the partner quiz don't exactly match. When this occurs, I take the time to discuss the many issues we face with this problem:

Do we need to enter all the data on this problem to generate a line of best fit? Or is there a faster way?

Why does the equation on the calculator not match the equation choices given?

This conversation brings out the idea that we can quickly sketch the choices give to see which line best fits the data. In fact, I designed this problem to encourage students to estimate the line of best fit. The cumbersome process of entering data is not needed. (I also use this as an opportunity to spiral back to linear functions and the simple process of reading slope as movement up and over on a graph).

Then, we discuss the disparity between the equation given on the graphing calculator and the answer given.

Why is the slope about 1.6 on the graphing calculator and 3/2 in the choices?

Are these close enough? Can we tell which one is better?

Students tend to agree that these slopes are close enough for the purpose of this question. I hope that they will also point out that those differences magnify on a larger scale. I usually show this on Geogebra. We quickly graph both lines and then scroll and zoom to higher x values and they can see how far apart the two lines become.

I want my students to understand that there is a limit to the precision we can reach by hand. Our line might like it has minimized the distance to all the points, but slight discrepancies can be impossible to detect by visual inspection.

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I like to give an exit ticket at the end of this lesson to see how my students are doing with the content. The initial investigation and partner quiz generally doesn't give me enough information to move forward. So I reserve the last 10 minutes of class for some independent time to work on the exit ticket: Line of Best Fit Exit Ticket.docx

My students will leave class as they finish. I plan to review the Exit Ticket at the start of the next class.